Daryl,
The information that George & Abigail were both alive in 1873 seems to fit with the possible deaths I have suggested you look at.
George Tedford?s marriage to Sarah Cooper was registered in Belfast Apr ? Jun 1909 Vol 1, page 436.
On the births computer system at GRONI, Belfast, it is possible to search using the fathers? surname and the mother?s maiden name, leaving the childs forename blank, and this throws up all children to that couple (or any other couple with the same names, as sometimes happens). Looking at the on-line indexes there were about 12 children born in Belfast in the period 1911 ? 1921 of the surname Tedford.
You could order copies of all those certificates to see if any were your family. Otherwise you?ll need to contact GRONI (or get a researcher to go there for you). If you go in person, GRONI charge ?14 to access the indexes. That includes 2 free readovers. Subsequent readovers are ?4 each. I am not sure what the fees are if you e-mail them (or ring them). You could ring them up and find out. You can pay over the phone with a debit or credit card.
The records for Northern Ireland on Familysearch and other similar sites all stop at 31.12.1921. Nothing is on-line after that. So if the couple had children after that date, the only way you will find out is by contacting GRONI.
George may not have stayed in Ireland of course. Hartland & Wolff had yards in Glasgow and Liverpool as well as Belfast and they often moved skilled staff between the yards, as required. So he may only have stayed in Belfast for a few years before moving on.
Incidentally, if he was working for Harland & Wolff, and was in Belfast in 1909 ? 1911, then George almost certainly worked on the Titanic.
Elwyn